Modeling of critical experiments and its impact on integral covariance matrices and correlation coefficients

Abstract

In this manuscript we study the modeling of experimental data and its impact on the resulting integral experimental covariance and correlation matrices. By investigating a set of three low enriched and water moderated UO 2 fuel rod arrays we found that modeling the same set of data with different, yet reasonable assumptions concerning the fuel rod composition and its geometric properties leads to significantly different covariance matrices or correlation coefficients. Following a Monte Carlo sampling approach, we show for nine different modeling assumptions the corresponding correlation coefficients and sensitivity profiles for each pair of the effective neutron multiplication factor k eff . Within the 95% confidence interval the correlation coefficients vary from 0 to 1, depending on the modeling assumptions. Our findings show that the choice of modeling can have a huge impact on integral experimental covariance matrices. When the latter are used in a validation procedure to derive a bias, this procedure can be affected by the choice of modeling assumptions, too. The correct consideration of correlated data seems to be inevitable if the experimental data in a validation procedure is limited or one cannot rely on a sufficient number of uncorrelated data sets, e.g. from different laboratories using different setups etc.

Analysis of experimental series of plutonium nitrate in aqueous solution and their correlation coefficients

“…Their uncertainties due to nuclear data uncertainties are clearly dominant over the uncertainties due to system parameters. This was already found for the LEU-COMP-THERM experiments in references [5,6,7,8].…”

“…In general, the correlation values range from slightly negative values to 0.7, but most correlation coefficients are in the range of [−0.1, 0.3]. Since the error of corr is in the range of 0.1 for values around corr = 0 for the used 250 samples [7], most correlations between experiments can be considered statistically not or only slightly significant. Higher correlation coefficients can be found within the experimental series PST-03 (experiments 03 to 08), PST- Comparing the results shown in figure 6 with figure 3 one can see, that almost all blocks of higher correlations are due to the same wt % 240 Pu.…”

“…For the generation of the randomly varied parameters a SUnCISTT add-on was used, which was developed in the course of this work and the works presented in references [5,6,7,8]. The add-on allows to create the random numbers using a configuration file for each experiment.…”

“…tanks, fuel rods or solutions. This can lead to significant correlations between experiments which in some cases have to be considered when determining safety margins [3,4,5,6,7]. One possibility to quantify the degree of linearity between two quantities X and Y (e.g.…”

“…The work presented in this paper was motivated by recent contributions of our group to a Benchmark defined by the Expert Group on Uncertainty Analysis for Criticality Safety Assessment (EGUACSA), a subgroup of the Working Party on Nuclear Criticality Safety (WPNCS) within the the Nuclear Energy Agency of the Organisation for Economic Co-operation and Development (OECD-NEA) [5,6,7,8]. The Benchmark entitled "Role of Integral Experiment Covariance Data for Criticality Safety Validation" [9] discusses the influence of experimental uncertainties, covariances and correlations between critical benchmark experiments used for validation, bias and safety limits determination.…”